Abstract. A Dirichlet problem for a singularly perturbed steady-state convection-diffusion equation with constant coefficients on the unit square is considered. In the equation under consideration the convection term is represented by only a single derivative with respect to one coordinate axis. This problem is discretized by the classical five-point upwind difference scheme on a rectangular pi...

In this paper we consider numerical methods for a singularly perturbed reaction–diffusion problem with a discontinuous source term. We show that such a problem arises naturally in the context of models of simple semiconductor devices. We construct a numerical method consisting of a standard finite difference operator and a non-standard piecewise-uniform mesh. The mesh is fitted to the boundary ...

This paper deals with a non-standard implicit finite difference scheme that is defined on quasi-uniform mesh for approximate solutions of the Magneto-Hydro Dynamics (MHD) boundary layer flow an incompressible fluid past flat plate wide range magnetic parameter. The proposed approach allows imposing given conditions at infinity exactly. We show how to improve obtained numerical results via refin...

A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function identified which matches the discontinuity in and also satisfies homogenous differential equation associated problem. The difference between this analytical solution approximated numerically, using an upwind finite operator combined appropriate layer-ada...

Simulation-driven design has become an effective methodology for improving the design process, in terms of both time and cost. Visualization of simulation results with high efficiency and fidelity is of significant importance for this methodology especially for the multidisciplinary simulation of complex products. One of the key challenges is to display and view multidisciplinary simulation res...

the present study deals with the analysis of the effects of radiative heat transfer of micropolar fluid flow over a porous and stretching sheet in the presence of magnetic field. the dynamic viscosity and thermal conductivity coefficient have formulated by temperature-dependent relations to obtain more exact results. the flow is supposed two-dimensional, incompressible, steady and laminar and t...

The singularly perturbed parabolic boundary value problem is considered. Difference scheme is obtained by using cubic spline difference scheme on Shishkin’s mesh in space and classical discretization on uniform mesh in time. To obtain better stability and simpler matrix the fitting factor in polynomial form is used. The uniform convergence is achieved. Numerical results are presented. AMS Mathe...

We study the stability of explicit one-step integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissible time step is tight for any mesh and any diffusion matrix within a factor of 2(d + 1), where d is the spatial dimension. Both full mass matrix and mass lumping are considered. The bound reveals that the stability c...

Two-dimensional (2-D) mesh-based motion compensation preserves neighboring relations (through connectivity of the mesh) as well as allowing warping transformations between pairs of frames; thus, it effectively eliminates blocking artifacts that are common in motion compensation by block matching. However, available 2-D mesh models, whether uniform or non-uniform, enforce connectivity everywhere...

Mortar method is proposed to form a macroscopic model for a problem with a multiscale conductivity. The macroscopic model is built on the coarse uniform grid quipped for the problem domain. For each uniform grid, artificial neighboring cells are attached to form a model which includes the localized microscale model. For the proposed model, a very fine mesh is introduced to resolve the microscal...